The Gordon growth model (GGM) is a commonly used version of the dividend discount model (DDM). The model is named after finance professor Myron Gordon and first appeared in his article 'Dividends, Earnings and Stock Prices,' which was published in the 1959 edition of Review of Economics and Statistics.

The GGM is mainly applied to value mature companies that are expected to grow at the same rate forever. The Gordon growth model, like other types of dividend discount models, begins with the assumption that the value of a stock is equal to the sum of its future stream of discounted dividends. The Gordon growth model formula is shown below:

Stock Price = D (1+g) / (r-g)

where,

D = the annual dividend
g = the projected dividend growth rate, and
r = the investor's required rate of return.

Let's look at an example. Suppose that Stock A pays a \$1 annual dividend and is expected to grow its dividend 7% per year. The investor's required rate of return is 8%. Plugging those numbers into the GGM formula gives you:

Value of Stock A = (\$1 * (1 + 0.07))/ (0.08 - 0.07) = \$107

To apply the Gordon growth model, you must first know the annual dividend payment and then estimate its future growth rate. Most investors simply look at the historic dividend growth rate and make the assumption that future growth will be comparable to past growth. But estimating your required rate of return for the stock, also known as the 'hurdle rate' or 'cost of capital' is a bit more challenging and requires a few more items of information.

Calculating Required Rate of Return

The concept of required rate of return begins with the idea that, all other things being equal, investors will demand higher rates of return for investments that carry more risk. The required rate of return calculation takes into account what you could be earning from a risk-free investment (the risk-free rate), the market rate of return and the risk specific to that particular stock as measured by the volatility of its share price.

Investors often substitute the U.S. Treasury bill rate for the risk-free rate. For the market rate, most investors use the historic annualized return from a broad stock index such as the S&P 500. If you are mathematically inclined, you can measure the specific risk associated with the stock by calculating the standard deviation of its share price, but most investors simply rely on the stock's 'beta' as supplied by financial news outlets like Bloomberg and Yahoo! Finance.

Once you have the three inputs, you can calculate required rate of return using the formula provided below:

Required rate of return = Risk free rate + Beta * (Market rate risk - Risk free rate)

Let's look at an example. Assume Treasury bills currently yield 2%, the broad stock market is expected to return 10% and Stock A has a beta of 1.3. The required rate of return for Stock A is:

Required rate of return for Stock A = 2 + 1.3 (10 – 2) = 12.4%

Model Strengths and Weaknesses

The Gordon growth model's greatest strength is its simplicity, but this can also be a disadvantage. Only a handful of factors are considered in the valuation and numerous assumptions must be made. For example, the formula assumes a single constant growth rate for dividends. In the real world, however, dividend growth often changes from year to year for a variety of reasons. Companies may choose to conserve cash during industry downturns or spend cash to make an acquisition. In either case, the dividend growth rate would likely be at least temporarily affected.

The Gordon growth model is also very sensitive to a required rate of return that is too close to the dividend growth rate. In the example below, Stock B has a dividend growth rate of 6% and Stock A has a 7% dividend growth rate. Both stocks pay a \$1 dividend and have a required rate of return of 8%, yet the 1% difference in dividend growth rates makes Stock B twice as valuable as Stock A.

Value of Stock B = \$1 * 1.06/ (.08-.06) = \$53

Value of Stock A = \$1 * 1.07/ (.08-.07) = \$107

However, if the dividend growth rate is far more or far less than the required rate of return, then the difference in the value of two stocks growing dividends 1% apart is much smaller. For example, suppose Stock B grows dividends at 1% a year and Stock A grows dividends 2% a year. Both stocks pay a \$1 dividend and have a required rate of return of 8%. As shown in the calculations below, the difference in the values of Stock A and Stock B in the low dividend growth scenario is modest -- only about 15%.

Value of Stock B = \$1 * 1.01/ (0.08-0.01) = \$14.43

Value of Stock A = \$1 * 1.02/ (0.08-0.02) = \$17

Despite a few shortcomings, the Gordon growth model continues to be widely used and especially popular for valuing companies in industries like banking and real estate, where dividend payments can be large and growth is relatively stable. The model is useful because it relies on inputs that are readily available or easy to estimate. However, investors shouldn't rely solely on the Gordon growth model for valuing stocks. Instead, the model should be used in conjunction with a SWOT analysis that takes into account non-financial factors like brand strength and patents, which don't fit into the model but have influence on the value of a stock.